Perform the indicated operation and simplify.
1. 1/4 + 1/3 = 2/3
2. 4/7 - 5/6 = 1/6
3. 3/5 * -4/7 = -12/35
4. 10/11 divided by 2/3 = 15/11
1/3 + 1/3 = 2/3
so how can 1/4 + 1/3 = 2/3 ?
6/6 - 5/6 = 1/6
so how can 4/7 - 5/6 = 1/6 ?
#3,4 are ok
1. 1/4 + 1/3
(1*3)/(4*3) + (1*4)/(3*4)
3/12 + 4/12
7/12 (not 2/3)
To perform the indicated operations and simplify, follow these steps:
1. Addition of fractions:
To add fractions, follow these steps:
- Find a common denominator by finding the least common multiple (LCM) of the denominators.
- Convert both fractions to have the same denominator.
- Add the numerators together to get the numerator of the sum.
- Keep the common denominator as the denominator of the sum.
In the first problem, 1/4 + 1/3:
- The LCM of 4 and 3 is 12.
- Convert 1/4 to 3/12 by multiplying the numerator and denominator by 3.
- Convert 1/3 to 4/12 by multiplying the numerator and denominator by 4.
- Add the numerators: 3 + 4 = 7.
- The sum is 7/12.
2. Subtraction of fractions:
To subtract fractions, follow these steps:
- Find a common denominator by finding the least common multiple (LCM) of the denominators.
- Convert both fractions to have the same denominator.
- Subtract the numerators to get the numerator of the difference.
- Keep the common denominator as the denominator of the difference.
In the second problem, 4/7 - 5/6:
- The LCM of 7 and 6 is 42.
- Convert 4/7 to 24/42 by multiplying the numerator and denominator by 6.
- Convert 5/6 to 35/42 by multiplying the numerator and denominator by 7.
- Subtract the numerators: 24 - 35 = -11.
- The difference is -11/42, which can be simplified by dividing both the numerator and denominator by their greatest common divisor (gcd), which is 1 in this case.
3. Multiplication of fractions:
To multiply fractions, follow these steps:
- Multiply the numerators to get the new numerator.
- Multiply the denominators to get the new denominator.
- Simplify the fraction if possible.
In the third problem, 3/5 * -4/7:
- Multiply the numerators: 3 * -4 = -12.
- Multiply the denominators: 5 * 7 = 35.
- The product is -12/35, which cannot be further simplified.
4. Division of fractions:
To divide fractions, follow these steps:
- Invert the second fraction by swapping the numerator and denominator.
- Multiply the fractions using the multiplication rules described above.
- Simplify the fraction if possible.
In the fourth problem, 10/11 divided by 2/3:
- Invert 2/3 to get 3/2.
- Multiply the fractions: 10/11 * 3/2.
- Multiply the numerators: 10 * 3 = 30.
- Multiply the denominators: 11 * 2 = 22.
- The product is 30/22, which can be simplified by dividing both the numerator and denominator by their greatest common divisor (gcd), which is 2 in this case.
- Simplified, the result is 15/11.